AMP - 18 Afterward Paul remained many days longer, and then told the brethren farewell and sailed for Syria; and he was accompanied by Priscilla and Aquila. At Cenchreae he [Paul] cut his hair, for he had made a vow.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
According to Matthew Henry's commentary: The cutting of hair according to Nazarite vow was those that lived in Judea were, in such a case, bound to do it at the temple: but those who lived in other countries might do it in other places. The Nazarite’s head was to be shaved when either his consecration was accidentally polluted, in which case he must begin again, or when the days of his separation were fulfilled (Num. 6:9 Num. 13:18 ), which, we suppose, was the case here. I tend to agree with Henry's analysis.
Paul taking a Nazarite vow according to Num chapter 6 is all well and good. The "pink elephant in the room" is WHY would he do this post-resurrection? Didn't sacrifices come to an end in Jesus?